In this paper, we investigated some properties of the closed lattices and gave their characterizations. The relationship between the Locale and the closed lattice was investigated. It is proved that the Cartesian product of the close lattice is still closed lattice. Moreover, we obtained the result that the closed lattice under a surjective map preserving arbitrary sups is still the closed lattice. Finally, we studied the property of the image of the closed lattice under the closure operator.